Open-loop control ($u(t)=u(t;x_0)$)

An open-loop control is prescribed as a function of time, possibly after calculation from an initial state and a dynamical model. It is executed without using observations of the actual current state to change the input. A simulated feedback control law can generate an open-loop waveform, but the resulting laboratory control does not automatically correct errors in the actual state or model.

For the ideal controlled plant with $w=0$, plan the control inputIntegration gives $x(t)=\min (t,1)$, so the planned command reaches the reference signal $r=1$ at $t=1$. If an unplanned constant control disturbance $w=0.2$ begins at $t=2$, the same open-loop control gives $x(t)=1+0.2(t-2)$ for $t\ge 2$: $x(4)=1.4$ and $x(8)=2.2$. Knowing the nominal response did not provide a way to correct the actual plant output.